This is a hard one. Depends where you live but due to € and £ I assume you are from Europe. To build a missile car to fit your budget would come down to base car price. If you spend 2k€ on base car, than you don't have much room for improvement. Another consideration is also if have tools and knowledge to work on your car by yourself or perhaps if you have friends who have and are prepared to work for beer and pizza. Otherwise the room gets ever tighter.
My advise would be an BMW 3 series either e36 or e46 with a straight 6. I would go with M50b25 with 5 series ZF gearbox, cheap, reliable, decent power. For a bit extra response you can fit and lighter M20 or S14 flywheel and clutch unit. Strip the interior fit a bucket seat for yourself and racing seatbelts, racing steering wheel is good to have too but not necessary, weld the diff. and refresh brakes front and rear with some better brake pads and discs. Get lots of rims and do a stud conversion at least on the rear where you will be changing wheels very often. If you can afford some coilovers than do that as well. Replacing all the suspension bushings is a good idea too.
This would be a basic missile car that would fit your budget. There are surely things I forgot mentioning. This things tend to escalate very quickly. Plus there are the worst ( the hidden) things, things you don't plan. Perhaps and engine needs some care, or maybe there is some rust to fix or you have some leaky exhaust. Things you have to take care and they cost time and money...
Best regards
Rok
